We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent. 1. Introduction In congestion situations of day-to-day as well as industrial problems, it has been realized that queueing models with phase service play vital role in depicting and analyzing queueing situations. Our aim in this paper is to provide an overview on the conceptual aspects for the phase service queueing models in different frameworks. In traditional queueing models, all arriving customers/jobs require main service which is to be completed in single phase. In many real time systems the service may be completed in many phases. The concept of optional phase services has been studied by many researchers for improving the grade of service. Sometimes only a few arriving customers require the optional services along with essential service for their satisfaction. Queueing models with phase service accommodate the real-world situations more closely. The purpose of present paper is to provide overview of queueing models with phase service and its applications in real life queueing problems. The motivation for studying the queueing systems with phase service comes from numerous versatile applications in the performance evaluation and dimensioning of production and manufacturing systems, computer and communication networks, inventory and distribution systems, and so forth. During the last few decades, attention has been paid increasingly by many researchers in studying the phase service queueing models. Many developments have taken place from time to time in this field and need further research in this regard. Various studies on phase service queueing models have appeared during literature 80’s
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